Sequences and Series

Things to remember:

Arithmatic sequences:

4,9,14,19,24…
10,8,6,4,2…

T1= first term
d= difference

Equations to use:

tn= t1 + d(n-1)

-t1 + tn
———-   = n
d

Arithmatic Series:

31+35+39+43…
12-9-6-3…

equations to use:

n(t1 + tn)
Sn= ———–
2

n[2t1 + d(n-1)]
Sn=  —————–
2

 

Geometric Sequences:

2,4,8,16,32…

2,1,1/2,1/4…

2,-4,8,-16,32…

r= common ratio
t1= first term

types: Finite= 2,6,18,54,162      Infanete= 2,6,18,54,162…        Convergent= 2,1, 1/2, 1/4, 1/8, 1/16…         Divergent= 2,-4,8,-16,32…

Equations:

tn= t1 x r^n-1

Geometric Series:

8+24+72+216…

equations to use:

t1(rⁿ  -1)
Sn= ———–
r – 1

rtn-t1
Sn= ———-
r – 1

 

Infanete series:

-1, -3/4, -9/16, -27/64…

2 + 3 + 4.5 + 6.75…

 

equations to use:

t1
S∞= —–
1 – r

S∞(1-r) = t1